Question 165394: Find the standard deviation. 44, 90, 73, 65, 76, 22, 50, 45, 37
Answer by Edwin McCravy(20081)   (Show Source):
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List them in a column headed x
Draw a line and add the column
x
44
90
73
65
76
22
50
45
37
-----
502
Divide the 502 by 9, the number of numbers
x
44
90
73
65
76
22
50
45
37
-----
9)502
----
55.777···
_
That is the mean, x. Subtract it from every value,
and place it in a column just to the right:
_
x x-x
44 -11.77···
90 34.22···
73 17.22···
65 9.22···
76 20.22···
22 -33.77···
50 -5.77···
45 -10.77···
37 -18.77···
-------------------
9)502
----
55.777···
Square every term in that column, and
place those in a column to the right,
and add them:
_ _
x x-x (x-x)²
44 -11.77··· 138.716
90 34.22··· 1171.160
73 17.22··· 296.605
65 9.22··· 85.049
76 20.22··· 408.938
22 -33.77··· 1140.938
50 -5.77··· 33.383
45 -10.77··· 116.160
37 -18.77··· 352.605
---------------------------
9)502 3743.554
----
55.777···
Divide that by 1 less than 9, or 8
467.944
---------
8)3743.554
Take the square root of 467.944
The standard deviation, s, is 21.632.
Edwin
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